A261500 Number of necklaces with n white beads and 6*n black beads.

1, 1, 7, 64, 735, 9276, 124936, 1753074, 25366335, 375677659, 5667212132, 86775157140, 1345153548264, 21069043965984, 332927800269694, 5301031234085664, 84967018635587775, 1369846562874360887, 22199151536133457885, 361411377745122110422, 5908312923795257331460

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..800

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]

Eric Weisstein's World of Mathematics, Necklace

Wikipedia, Necklace (combinatorics)

Index entries for sequences related to necklaces

Formula

a(n) = 1/(7*n) * Sum_{d|n} C(7*n/d,n/d) * A000010(d) for n>0, a(0) = 1.

a(n) ~ 7^(7*n-1/2) / (2 * sqrt(3*Pi) * 6^(6*n) * n^(3/2)). - Vaclav Kotesovec, Aug 22 2015

Maple

with(numtheory):
a:= n-> `if`(n=0, 1, add(binomial(7*n/d, n/d)
             *phi(d), d=divisors(n))/(7*n)):
seq(a(n), n=0..25);

Crossrefs

Column k=6 of A261494.

Sequence in context: A293470 A256506 A008787 * A173516 A197785 A360465

Adjacent sequences: A261497 A261498 A261499 * A261501 A261502 A261503

Keyword

nonn

Author

Alois P. Heinz, Aug 21 2015

Status

approved